Payout formula

If the actual price falls within the predicted range, the bet wins and is rewarded from the token's reserve using a computed multiplier, in addition to returning it. Core formula is

$$\text{Payout} = \min(\text{Reserve Liquidity}, \text{Stake} + \text{Stake} \times \text{Prediction Quality}) + \text{Reserve Bonus}$$

Where:

• Prediction Quality is a multiplier coefficient computed at betting time

• Reserve Liquidity is cap enforcement computed at resolution time

Prediction Quality components are

• Range Sharpness = (High - Low) / Current Price

• Boldness = 1 - Local Confidence

• Lead Time = Resolution Time - Placement Time

The multiplier formula:

$$\text{Prediction Quality} = \text{Scaling Factor} \times (\text{Lead Time Quality})^{w_L} \times (\text{Boldness Quality})^{w_B} \times (\text{Sharpness Quality})^{w_S}$$

Initial Monte Carlo simulation suggested Scaling Factor of 1 at project launch with the Weights set to 1/3. See quality calculations and their suggested launch configs in the ‘Key parameters’ section.

We use exponential weighting (i.e. raising each quality score to a weight) instead of additive weighting to compute overall Prediction Quality. This approach reflects the intuition that a strong prediction must balance timeliness, conviction, and precision, and excelling in one area cannot fully compensate for weakness in another.

Reserve Liquidity is simply its size that caps edge case payouts.

The payout system ensures that winning bets are fully covered by the token’s current reserve:

• At the moment of betting, the system checks whether a bet’s calculated payout based on its Prediction Quality score is fully covered by the reserve. If not, the bet is rejected.

• At the moment of resolution, the system checks whether a payout will drain the reserve in spite of its initially calculated safety. If so, it pays out as much as possible, waives the remainder, and attributes the difference to risk.

Reserve Bonus aims to evenly distribute the surplus funds to high-quality winning bets:

$$\text{Reserve Bonus} = (\text{Reserve Liquidity} - \text{Target Level}) \times \text{Bonus Share}$$

Bonus Share determines what portion of the available reserve surplus a winning bet receives, favoring more accurate and timely predictions while maintaining long-term reserve health.

Naturally, Reserve Bonus is capped by the available bonus pool on top of Target Level.